Aluminoxanes find use as components in polymerization and oligomerization catalysts. Aluminoxanes have been prepared by reacting a hydrocarbon solution containing trialkyl aluminum with hydrated crystalline salts such as CuSO.sub.4.5H.sub.2 O ("Mechanism of Stereochemical Control in Propylene Polymerization with Soluble Group 4B Metallocene/Methylalumoxane Catalysts, J. Am. Chem. Soc., 1984, 106, 6355-6364) and Al.sub.2 SO.sub.4.9H.sub.2 O ("Zirconium Catalysts Polymerize Olefins Faster," Chem. & Eng. News, July 4, 1983, 29-30 and U.S. Pat. No. 4,544,762, issued Oct. 1, 1985). This technique requires guarding against the possibility of contaminating the aluminoxanes with small amounts of the crystalline salts which can act as poisons when the aluminoxanes are used in polymerization catalysts. In U.S. Pat. No. 3,300,458, issued Jan. 24, 1967 a method is disclosed for preparing aluminoxanes which consists of contacting trialkyl aluminum dissolved in a hydrocarbon solvent with a second hydrocarbon stream which has been saturated with water by contacting the solvent with water in a solvent saturator. In this technique, however, since the amount of water present in the hydrocarbon is small, being limited by the solubility of water in the solvent, relatively large amounts of solvent are required to prepare the aluminoxanes. Manyik et al in "A Soluble Chromium-based Catalyst for Ethylene Trimerization of Polymerization", Journal of Catalysis, 47, 197-209, (1977) also discloses the use of water wetted solvent and further discloses the use of the direct addition of water to a dilute solution of trialkyl aluminum. However, the water addition must be done very slowly in order to prepare the aluminoxane rather than aluminum hydroxide. One method for avoiding the problems that result from the use of water-wetted solvents and direct addition of water is to use the sonification procedure disclosed in co-pending application Ser. No. 896,689, filed 8/15/86. Another method is to use the process of the instant invention whereby water is dispersed in an organic solvent utilizing high speed stirring.